Mr Clark spoke with Broadwater Warren reserve owners, the Royal Society for the Protection of Birds, to ask why options for cycling in the area had not been explored in more detail.
He met RSPB regional director Chris Corrigan, the charity's spokesman Adrian Thomas, cyclist Tim Dauncey, and Conrad Froud of local pro-cycling group Hubs and Spokes.
The meeting was arranged following an outcry from East Sussex cyclists when it was decided cycling was banned from the site.
Tunbridge Wells MP Mr Clark said: "We talk about quiet enjoyment sites and that must be part of the objective people can appreciate the environment that's there. Just to say no cyclists just seems ludicrously Draconian."
He questioned why the track around the reserve could not become a public bridleway for horse riders, cyclists and pedestrians.
He also suggested creating a separate cycle path through the reserve, or splitting the existing path.
Mr Corrigan said that when the RSPB took over the land, it also took on the liability for any accidents occuring on it.
Mr Clark said: "I have not heard a single complaint about conflict between a walker and a cyclist using a bridleway, not one."
Mr Corrigan said: "Cyclists do come into conflict with walkers, you might not get complaints but we get complaints and our site staff have to manage them. If you think, 'What's the purpose of the RSPB?' then it is not to provide cycling facilities."
The RSPB says "alarm bells" rung about cycling in the forest as they calculated its regeneration programme at the reserve could see around 30,000 visits a year and around 14,000 separate visitors.
Questioning the way in which the RSPB has handled the issue, Mr Dauncey said: "If one of the most difficult areas is management of people, you have got the experience through a number of reserves and therefore there must be a number of solutions to deal with that."
Mr Clark has been involved in recent campaigns to introduce more cycling routes in Tunbridge Wells.
He said: "It's perfectly possible, you have this space here and you don't even have cars."
Mr Dauncey suggested having a RSPB permit for cyclists using the reserve to cover the cost of the new track.
It was agreed the RSPB would find out the cost of creating a separate track, as well as looking at other options in more detail.